Problem: You are given an unweighted tree with n vertices. Recall that a tree is a connected undirected graph without cycles.

Your task is to choose three distinct vertices a, b, c on this tree such that the number of edges which belong to at least one of the simple paths between a and b, b and c, or a and c is the maximum possible. See the notes section for a better understanding.

The simple path is the path that visits each vertex at most once.

Input

The first line contains one integer number n (3 ≤ n ≤ 2 ⋅ 10^5) — the number of vertices in the tree. 

Next n - 1 lines describe the edges of the tree in form a_i, b_i (1 ≤ a_i, b_i ≤ n, a_i ≠ b_i). It is guaranteed that given graph is a tree.

Output

In the first line print one integer res — the maximum number of edges which belong to at least one of the simple paths between a and b, b and c, or a and c.

In the second line print three integers a, b, c such that 1 ≤ a, b, c ≤ n and a ≠, b ≠ c, a ≠ c.

If there are several answers, you can print any.

Example

Input


8
1 2
2 3
3 4
4 5
4 6
3 7
3 8


Output


5
1 8 6

Note

The picture corresponding to the first example (and another one correct answer):

<image>

If you choose vertices 1, 5, 6 then the path between 1 and 5 consists of edges (1, 2), (2, 3), (3, 4), (4, 5), the path between 1 and 6 consists of edges (1, 2), (2, 3), (3, 4), (4, 6) and the path between 5 and 6 consists of edges (4, 5), (4, 6). The union of these paths is (1, 2), (2, 3), (3, 4), (4, 5), (4, 6) so the answer is 5. It can be shown that there is no better answer.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;

public class ThreePathsOnATree {
    public static void main(String[] args) {
        FastScanner scanner = new FastScanner();
        PrintWriter out = new PrintWriter(System.out,false);
        int n= scanner.nextInt();
        ArrayList<Integer>[] graph = new ArrayList[n];
        for(int i = 0; i < n; i++) graph[i] = new ArrayList<>();
        for(int i = 1; i < n; i++) {
            int a = scanner.nextInt()-1;
            int b = scanner.nextInt()-1;
            graph[a].add(b);
            graph[b].add(a);
        }
        int[] dists = new int[n];
        Arrays.fill(dists, -1);
        dists[0] = 0;
        ArrayDeque<Integer> queue = new ArrayDeque<>();
        queue.offer(0);
        while(!queue.isEmpty()) {
            int cur = queue.poll();
            for(int edge: graph[cur]) {
                if (dists[edge] == -1) {
                    dists[edge] = dists[cur] + 1;
                    queue.offer(edge);
                }
            }
        }
        int max = 0;
        for(int i = 1; i < n; i++) {
            if (dists[max] < dists[i]) {
                max = i;
            }
        }
        Arrays.fill(dists, -1);
        dists[max] = 0;
        queue.offer(max);
        int[] par = new int[n];
        while(!queue.isEmpty()) {
            int cur = queue.poll();
            for(int edge: graph[cur]) {
                if (dists[edge] == -1) {
                    dists[edge] = dists[cur] + 1;
                    par[edge] = cur;
                    queue.offer(edge);
                }
            }
        }
        int diam = 0;
        for(int i = 0; i < n; i++) {
            if (dists[diam] < dists[i]) {
                diam = i;
            }
        }
        int curp = diam;
        int ans = dists[diam];
        Arrays.fill(dists, -1);
        while(curp != max) {
            queue.offer(curp);
            dists[curp] = 0;
            curp = par[curp];
        }
        queue.offer(curp);
        dists[curp] = 0;
        while(!queue.isEmpty()) {
            int cur = queue.poll();
            for(int edge: graph[cur]) {
                if (dists[edge] == -1) {
                    dists[edge] = dists[cur] + 1;
                    queue.offer(edge);
                }
            }
        }
        int last = 0;
        while(last == diam || last == max) last++;
        for(int i = 0; i < n; i++) {
            if (dists[last] < dists[i]) {
                last = i;
            }
        }
        ans += dists[last];
        max++; diam++; last++;
        out.println(ans);
        out.println(max + " " + diam + " " + last);
        out.flush();
    }
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }
        public FastScanner() {
            this(new InputStreamReader(System.in));
        }
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
        String readNextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}